Achef has 10 spice jars, but his new spice rack only holds 8 spice jars. how many ways can he arrange 8 jars on the spice rack?
a. 45
b. 80
c. 1,814,400
d. 3,628,800

He has 10 spice jars, but the spice rack only holds 8 spice jars.
Calculate in how many ways he can choose 8 spice jars from 10 spice jars using combination:


Each combination of 8 spice jars that he chooses he can arrange in 8! ways.

He can choose 8 spice jars in (10!)/(8!×2!) ways and arrange each combination in 8! ways.
Using the rule of product:


He can arrange 8 jars on the spice rack in c. 1,814,400 ways.